Given that #csctheta=-8/5# where #pi<theta<(3pi)/2#, how do you determine the exact value of #tantheta#?

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Given that #csctheta=-8/5# where #pi<theta<(3pi)/2#, how do you determine the exact value of #tantheta#?

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Answer 1 · 2017-06-07T10:42:23

# tan theta = 5/sqrt39#

Explanation:

#csc theta = -8/5 :. sin theta = -5/8 ; pi < theta <(3pi)/2, theta# is in third quadrant. Let #P = #perpendicular of rt triangle , #H=#hypotenuse of a rt. triangle and #B=# base of rt.triangle.

#Sin theta = P/H :. P = -5 ; H=8 :. B= sqrt(H^2-P^2)= sqrt(64-25)=+-sqrt39 = -sqrt39# In #3# rd quadrant both #P and B# are negative.

#:. tan theta = P/B = (-5)/-sqrt39 = 5/sqrt39# [Ans]

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Given that #csctheta=-8/5# where #pi<theta<(3pi)/2#, how do you determine the exact value of #tantheta#?

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